Lezaleas

Your risk of ruin can never be zero. I have no idea where you got 2500bb, there's absolutely nothing special about that number.
If the game is deeper your standard deviation (what you may call variance) will go you slightly up, like has been said before. Your winrate might go up a bit too. It may go up enough to offset most of the extra risk

This is no different in practice from heads up pots. When you hold a bluffcatcher and call against an opponent that never bluffs he's also making a mistake that reduces your ev. Multi way it's exactly the same. That doesn't mean that the solution is useless, just that you have to be careful in which situations to use it and in which situations to deviate. Unless you play some very hard games you should study gto mostly to know how to deviate and not how to play it anyways.

There's very little value on dominating our opponent weaker holdings. So when we look at TT we have 60% eq and we are really strong vs 99-22 etc. But we have 35% against the top of the SB range, which is the range that will give us action. And on any overcard it gets even worse. So let's be lenient and say that we win half the pot whenever we call with TT IP. We pay 7bb to win half of the 18bb resulting pot if the btn folds, so we win 9bb. But the btn should 4bet around 10% of the time so we are only winning around 1bb with our cold call. I'm pretty sure TT can win more than 1bb by raising when compared to our worst 4bet bluff so I'd rather raise. And TT is like the prime candidate for a call, everything else is doing worse. So yeah I don't see how we can start developing a calling range, we are simply being offered horrible pot odds, not closing the action, and any hand that can call is better off raising.
It's also really bad to have a small calling range that's too face up, we can't continue with just TT-99 and Ajs or something like that, we need to have many types of hands and all of those combined need to be played better this way, which means our TT and similar need to be strong enough to carry whatever we also call for balance

Ok yeah, that's true, but we still have to take a decision every time it's on us. Which combos of hands do we suspect of wanting to cold call?

How's our flop 3b range looking? This hand is much better there.
Also, his turn overbet is horrible and doesn't make any sense

I really don't understand which hand gains that much by cold calling over raising that makes you feel the need to develop a cold calling range. Like which combo is doing considerably better than a bluffcatcher and isn't better off raising?

I'm talking about equilibrium here

We block some straights and top/two pairs so it's an easy call. We really shouldn't be doing too much bluffcatching and calling otf when we don't close the action multiway, at least in theory. Continue mostly by raising a strong range that's ahead of the HJ value range, balanced with bluffs as usual

Btn vs BB, srp, 832r. Look at the ev with the btn combos of 99. And 1% pot is not a tiny margin, it's about 5bb/100 so not sure why you think it doesn't
matter

Edit: make sure to allow overbetting

1 - With the side pot, hero should only continue by raising. The bb shouldnt bluffcatch in this situation. When it calls it shouldnt have a balanced range. It has nutted hands only. So 2p+ and combo draws. Since it only has value we shouldnt ever bluffcatch, Since we never bluffcatch we only get into the pot when we think we are ahead(so sets), since we only get into the pot when we are ahead we only continue by raising. Weirdly enough, QQ makes a very good bluff tough, We are looking for bluffs that can win the pot against the ss if the bb fold. So we'd rather bluff with QQ instead of a draw that has more equity against the bb.

Now wheter we can trust the bb to understand all of this or not is another issue

I explained this in another response here, I think, but it's impossible that we ever have 0% bet fq at eq IP. As you said, his range is so strong here that he should cbet range. PIO can't say that you should never bet unless you node-lock him into some strat where he checks and we are not talking about eq then, in which case you may node-lock a range so strong that we never bet then. It's certainly likely that he's checking such a strong range. I just wanted to clarify that it never happens at eq.

Edit.: it's also impossible for IP to have a low betting frequency either, we should bet at least 45% when checked to, no matter how strong the initial OOP range was. You can check this in your solver

His line doesn't make any sense, he should bet range small the flop. As played he shouldn't overbet the turn either, his range is pretty dense on JJ-77 and similar that bets smalls and his traps should go into that range for protection.
I would exploitative fold like the other people are saying, because he's bombing the river at a high rate. But if I his line hadn't been so horrible and I had more trust in his abilities this is a call turn fold river

This is wrong:
"we should probably be betting 0% on this flop when checked to (because it is such a strong board for the OOP player)"

If we are betting 0% he should never check a strong hand. So we can start betting then. I'm not saying it doesn't work exploitatively tough, just that at equilibrium we never check range IP

Im not sure what you are trying to say but thats exactly what I meant by exploitative folding, villain doesnt have enough bluffs. Unless you are trying to say that he shouldnt have enough bluffs even at equilibrium, in which case I disagree but I can see your point, its close

Your play is great in theory but I wouldnt trust an average low stakes player to find enough bluffs on this spot. I would exploitatively fold

The exploitative adjustment is to always fold our bluffcatchers. Folding at a frequency slightly bigger than required is a minimally exploitative approach. I would strongly recommend a maximally approach Against recs, specially with lines like this that are almost always strong

There's a whale in the pot, easy fold

So you cant reply to replies or its just my phone? Anyways, I moved up from 1 to 100NL employing an aggressive bankroll management and, yes I had to move down stakes countless times, and it's super easy. If you don't have the discipline to move down stakes when required then you really need to work on your mental side since it's so important to be emotionally stable and disciplined if you want to have long-term success in poker

As for the math, at 90bb/100 and 3bbwrt we can consider 100 hands of poker a game where we win 93bb half of the time and we lose 87bb the other half. Then we use a kelly calculator. It wil return that we need about 26BI (I forgot already) but since stakes are discrete we want to stick to playing between 19-38BI, that mean we move up when we have 19BI. I made a python script to calculate all that stuff too. And you can't use risk of ruin because, yes, you can move down stakes at any time so it's like you have more "lives"

It depends on your winrate and variance. However, for an average variance (about 90bb/100) and a 3bb/winrate you should move up stakes as soon as you have around 19BI for the next stake. yes, that sounds much more aggressive than what you hear everywhere but it's what the math says. 50BI is way way too much unless your winrate is barely above breakeven, you are expected to move up at 40% the pace of a 19BI strategy

Ok, first of all, if you 5bet, there is only 1 sizing possible. You cant bet more than about 36% of your stack without having enough equity to stack off on A5s or a small pair against most ranges. It may be different this deep when his range is heavier on AA but you can probably still profitably call a shove after raising to 1k on your high eq bluffs so its either call or shove.

Lets work out what we are against here. ill assume he opens around 13% and 4bets around 17% and calls 33%, folding 50%. We risk 1400 if we shove A5s to win 800 plus we heavily block AA so he needs to stack with at least 40% of his 4bet. This is his value part, which he raised intending to stack off. 0.40.17.13, 0.9% so he's stacking with AA-KK. You have more equity shoving Axs against that so good call.

Now, on the flop,the whole hand gets harder because the SB shouldnt be play like this and its difficult to put him on a range. His play is just bad and shouldnt ever be made with any hand. I figure QQ and JJ are the most likely hands he's doing this with. We shouldnt bluffcatch if we dont close the action since he can have many nutted combos. However, KK is stronger than a 0ev bluffcatch here so, if the SB is as wide as you think he is, im on board with calling.

UTG 4bet range should look something like AA-KK and 18 combos of hands at a lower frequency like QQ-AK-Axs-SCs etc. So on the flop, he very rarely has a set, we block his KK value bets, and we beat any AQs or ATs type of hand. We are only scared of AA. which he has 18% of the time but should check at some frequency.

Lets say that we call and SB folds, since we folded our bluffcatchers our range looks something super strong like KK-QQ and some JJ and strong draws at a smaller frequency. If he bets at any runout that didnt improve most of his bluffs like an A turn, we MDF and end up with a 0ev call on KK. I suspect he should rangecheck any non A turn tough, and we try to showdown.

Yes, this was the correct play. Note that whenever there is a chop on board we have to bluff twice as much than normally. If you do the math, when we try to make his bluffcatchers(his chops in this case) iindifferent he only wins half as normal whenever he bluffcatches right, so we need to double our bluffs to cancel out that disadvantage and offer him the correct odds. Which means that any hand you would normally bluff should also be a bluff in a chop on board situation

1- Nothing wrong with our bet and sizing
2- The premise is wrong, this is not the micros, he should still have plenty of combos to fold
3- No, your overpairs benefit more from going for 2 or even 3 streets(he doesnt have that many draws)
4- The ev of shoving the turn is very close to 0, you can study your range to determine at which frequency you need to shove

Easy calll since we are the top of our range

Whenever we are polarized and the turn or river heavily improves our bluff range we commonly end up betting almost every bluff again. This one blocks JJs so it's even easier.

Are we seriously considering wheter to fold the 2nd nuts or not?
We understand that villain is aggro, plays high stakes and we are having a conversation that involves folding the second nuts with blocker to the nuts? Really?